This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. The Filter Diagonalization Method (FDM) is a recently developed signal processing algorithm based on quantum mechanic's mathematical formalism of the harmonic inversion problem. FDM is shown to provide extremely high precision in finding resonance frequencies with 1ppm accuracy on small number of transient data points e.g. 10k. It was used in frequency shift chasing experiments for the purposes of determining intra-transient frequency shifts and using them for reference deconvolution and study of space charge effect. In this study we used an in-house C++ implementation of the FFT Square Window FDM, which will be available as open source software in an upcoming release of the Boston University Data Analysis (BUDA) system. Theoretical spectra were generated by using in-house simulation software with 1 mega-point length and 1 MHz sampling rate. Real spectra of Substance P were acquired on homebuilt ESI FTMS instrument (1 mega-point length with 1MHz acquisition rate). Frequency chasing experiments were performed on transient domains ranging from 1000 to 20000 data points starting with the 0 offset and shifting depending on the experiment from 1 to 200 data points into the transient. Kwin used ranges from 4-11 points. FDM shows amazing precision and high resolution on small number of data points. FDM is much slower and not as stable as FFT and for that reason cannot compete directly with FFT. However FDM proves to be a good tool for reconstructing frequency shift plots. On theoretical spectra it showed ability to trace frequency shifts of .005 Hz with signal:noise ratio of 2. A substance P spectrum was used in the frequency chasing experiment (figure 1). The isotopic beat pattern is faithfully reproduced in both abundance and frequency shifts. Space charge, even for such a simple spectrum, are approximately 400 ppm even though post FFT, it is possible to get 1ppm mass accuracy on this spectrum. This result indicates that the FFT effectively averages out these cyclic frequency shifts to achieve its results. FDM, therefore, is a new tool for study space charge. The frequency shift plots, if they are shown to be consistent, could be used in reference deconvolution. The application of FDM in extreme space charge conditions, such as those caused by the famous "nipple effect" has been carried out. The results were recently published in JASMS (2009, 20, 247-256). The spontaneous loss of coherence catastrophe (SLCC), colloquially known as the "nipple effect", describes a phenomenon in FT-ICR mass spectrometry, where the transient collapses and dies out quickly, forming a nipple-like shape. Although SLCC is a frequently observed, space-charge related effect in FT-ICR MS, it is also one that is poorly studied. In this study, the FDM is used to study the SLCC. Because FDM's resolution depends not on the length of the transient signal, but rather on the local peak density, it is capable of operating on very short transients. It is also reliable under noisy conditions, and reproduces complete information about a peak. All of these factors make it an ideal technique for studying rapid space charge induced frequency modulations in FT-ICR MS. It was found that frequency spikes correlated with amplitude minima before the SLCC, which agreed with the known observation that frequency increases at lower space-charge conditions. The fact that this correlation flipped over at the SLCC suggested that the isotope ion packets were temporarily coming back into phase (high space charge) at the amplitude minima. It was proposed that this may occur only when the magnetron orbit diameter is similar to that of the cyclotron orbit. This claim was supported by the electron promoted ion coherence (EPIC) experiments, which showed that the SLCC is observed only when there is a strong magnetron component. These findings reinforced the need for reduction of magnetron drift and space-charge induced frequency modulation when pursuing the higher mass accuracy and resolving power capabilities of the FT-ICR MS. Using the FDM based frequency shift analysis, we have also shown the ability to determine how axial oscillations perturb the cyclotron frequency. This is a far smaller effect than the isotopic beat pattern effect previously shown, so in order to do it, we had to use a peak without isotopes, and Cesium Iodide was able to provide a nice cluster peak for just this purpose.